{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/master/gaussian_processes.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    # Check if notebook is running in Google Colab\n",
    "    import google.colab\n",
    "    # Get additional files from Github\n",
    "    !wget https://raw.githubusercontent.com/krasserm/bayesian-machine-learning/master/gaussian_processes_util.py\n",
    "    # Install additional dependencies\n",
    "    !pip install GPy==1.9.8\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian processes\n",
    "\n",
    "## Introduction\n",
    "\n",
    "In supervised learning, we often use parametric models $p(\\mathbf{y} \\lvert \\mathbf{X},\\boldsymbol\\theta)$ to explain data and infer optimal values of parameter $\\boldsymbol\\theta$ via [maximum likelihood](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) or [maximum a posteriori](https://de.wikipedia.org/wiki/Maximum_a_posteriori) estimation. If needed we can also infer a full [posterior distribution](https://en.wikipedia.org/wiki/Posterior_probability) $p(\\boldsymbol\\theta \\lvert \\mathbf{X},\\mathbf{y})$ instead of a point estimate $\\boldsymbol{\\hat\\theta}$. With increasing data complexity, models with a higher number of parameters are usually needed to explain data reasonably well. Methods that use models with a fixed number of parameters are called parametric methods. \n",
    "\n",
    "In non-parametric methods, on the other hand, the number of parameters depend on the dataset size. For example, in [Nadaraya-Watson kernel regression](https://en.wikipedia.org/wiki/Kernel_regression), a weight $w_i$ is assigned to each observed target $y_i$ and for predicting the target value at a new point $\\mathbf{x}$ a weighted average is computed: \n",
    "\n",
    "$$f(\\mathbf{x}) = \\sum_{i=1}^{N}w_i(\\mathbf{x})y_i$$\n",
    "\n",
    "$$w_i(\\mathbf{x}) = \\frac{\\kappa(\\mathbf{x}, \\mathbf{x}_{i})}{\\sum_{i'=1}^{N}\\kappa(\\mathbf{x}, \\mathbf{x}_{i'})}$$\n",
    "\n",
    "Observations that are closer to $\\mathbf{x}$ have a higher weight than observations that are further away. Weights are computed from $\\mathbf{x}$ and observed $\\mathbf{x}_i$ with a kernel $\\kappa$. A special case is k-nearest neighbors (KNN) where the $k$ closest observations have a weight $1/k$, and all others have weight $0$. Non-parametric methods often need to process all training data for prediction and are therefore slower at inference time than parametric methods. On the other hand, training is usually faster as non-parametric models only need to remember training data. \n",
    "\n",
    "Another example of non-parametric methods are [Gaussian processes](https://en.wikipedia.org/wiki/Gaussian_process) (GPs). Instead of inferring a distribution over the parameters of a parametric function Gaussian processes can be used to infer a distribution over functions directly. A Gaussian process defines a prior over functions. After having observed some function values it can be converted into a posterior over functions. Inference of continuous function values in this context is known as GP regression but GPs can also be used for classification. \n",
    "\n",
    "A Gaussian process is a [random process](https://en.wikipedia.org/wiki/Stochastic_process) where any point $\\mathbf{x} \\in \\mathbb{R}^d$ is assigned a random variable $f(\\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$ is itself Gaussian:\n",
    "\n",
    "$$p(\\mathbf{f} \\lvert \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\lvert \\boldsymbol\\mu, \\mathbf{K})\\tag{1}\\label{eq1}$$\n",
    "\n",
    "In Equation $(1)$, $\\mathbf{f} = (f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$, $\\boldsymbol\\mu = (m(\\mathbf{x}_1),...,m(\\mathbf{x}_N))$ and $K_{ij} = \\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$. $m$ is the mean function and it is common to use $m(\\mathbf{x}) = 0$ as GPs are flexible enough to model the mean arbitrarily well. $\\kappa$ is a positive definite *kernel function* or *covariance function*. Thus, a Gaussian process is a distribution over functions whose shape (smoothness, ...) is defined by $\\mathbf{K}$. If points $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are considered to be similar by the kernel the function values at these points, $f(\\mathbf{x}_i)$ and $f(\\mathbf{x}_j)$, can be expected to be similar too. \n",
    "\n",
    "A GP prior $p(\\mathbf{f} \\lvert \\mathbf{X})$ can be converted into a GP posterior $p(\\mathbf{f} \\lvert \\mathbf{X},\\mathbf{y})$ after having observed some data $\\mathbf{y}$. The posterior can then be used to make predictions $\\mathbf{f}_*$ given new input $\\mathbf{X}_*$:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{y}) \n",
    "&= \\int{p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{f})p(\\mathbf{f} \\lvert \\mathbf{X},\\mathbf{y})}\\ d\\mathbf{f} \\\\ \n",
    "&= \\mathcal{N}(\\mathbf{f}_* \\lvert \\boldsymbol{\\mu}_*, \\boldsymbol{\\Sigma}_*)\\tag{2}\\label{eq2}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Equation $(2)$ is the posterior predictive distribution which is also a Gaussian with mean $\\boldsymbol{\\mu}_*$ and $\\boldsymbol{\\Sigma}_*$. By definition of the GP, the joint distribution of observed data $\\mathbf{y}$ and predictions $\\mathbf{f}_*$  is\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\\mathbf{y} \\\\ \\mathbf{f}_*\\end{pmatrix} \\sim \\mathcal{N}\n",
    "\\left(\\boldsymbol{0},\n",
    "\\begin{pmatrix}\\mathbf{K}_y & \\mathbf{K}_* \\\\ \\mathbf{K}_*^T & \\mathbf{K}_{**}\\end{pmatrix}\n",
    "\\right)\\tag{3}\\label{eq3}\n",
    "$$\n",
    "\n",
    "With $N$ training data and $N_*$ new input data, $\\mathbf{K}_y = \\kappa(\\mathbf{X},\\mathbf{X}) + \\sigma_y^2\\mathbf{I} = \\mathbf{K} + \\sigma_y^2\\mathbf{I}$ is $N \\times N$, $\\mathbf{K}_* = \\kappa(\\mathbf{X},\\mathbf{X}_*)$ is $N \\times N_*$ and $\\mathbf{K}_{**} = \\kappa(\\mathbf{X}_*,\\mathbf{X}_*)$ is $N_* \\times N_*$. $\\sigma_y^2$ is the noise term in the diagonal of $\\mathbf{K_y}$. It is set to zero if training targets are noise-free and to a value greater than zero if observations are noisy. The mean is set to $\\boldsymbol{0}$ for notational simplicity. The sufficient statistics of the posterior predictive distribution, $\\boldsymbol{\\mu}_*$ and $\\boldsymbol{\\Sigma}_*$, can be computed with<sup>[1][3]</sup>\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\boldsymbol{\\mu_*} &= \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{y}\\tag{4}\\label{eq4} \\\\\n",
    "\\boldsymbol{\\Sigma_*} &= \\mathbf{K}_{**} - \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{K}_*\\tag{5}\\label{eq5}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This is the minimum we need to know for implementing Gaussian processes and applying them to regression problems. For further details, please consult the literature in the [References](#References) section. The next section shows how to implement GPs with plain NumPy from scratch, later sections demonstrate how to use GP implementations from [scikit-learn](http://scikit-learn.org/stable/) and [GPy](http://sheffieldml.github.io/GPy/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation with NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will use the squared exponential kernel, also known as Gaussian kernel or RBF kernel:\n",
    "\n",
    "$$\n",
    "\\kappa(\\mathbf{x}_i,\\mathbf{x}_j) = \\sigma_f^2 \\exp(-\\frac{1}{2l^2}\n",
    "  (\\mathbf{x}_i - \\mathbf{x}_j)^T\n",
    "  (\\mathbf{x}_i - \\mathbf{x}_j))\\tag{6}\n",
    "$$\n",
    "\n",
    "The length parameter $l$ controls the smoothness of the function and $\\sigma_f$ the vertical variation. For simplicity, we use the same length parameter $l$ for all input dimensions (isotropic kernel). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def kernel(X1, X2, l=1.0, sigma_f=1.0):\n",
    "    '''\n",
    "    Isotropic squared exponential kernel. Computes \n",
    "    a covariance matrix from points in X1 and X2.\n",
    "    \n",
    "    Args:\n",
    "        X1: Array of m points (m x d).\n",
    "        X2: Array of n points (n x d).\n",
    "\n",
    "    Returns:\n",
    "        Covariance matrix (m x n).\n",
    "    '''\n",
    "    sqdist = np.sum(X1**2, 1).reshape(-1, 1) + np.sum(X2**2, 1) - 2 * np.dot(X1, X2.T)\n",
    "    return sigma_f**2 * np.exp(-0.5 / l**2 * sqdist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other kernels that can be used for Gaussian processes. See \\[3\\] for a detailed reference or the scikit-learn documentation for [some examples](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prior\n",
    "\n",
    "Let's first define a prior over functions with mean zero and a covariance matrix computed with kernel parameters $l=1$ and $\\sigma_f=1$. To draw random functions from that GP we draw random samples from the corresponding multivariate normal. The following example draws three random samples and plots it together with the zero mean and the 95% confidence interval (computed from the diagonal of the covariance matrix)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from gaussian_processes_util import plot_gp\n",
    "\n",
    "# Finite number of points\n",
    "X = np.arange(-5, 5, 0.2).reshape(-1, 1)\n",
    "\n",
    "# Mean and covariance of the prior\n",
    "mu = np.zeros(X.shape)\n",
    "cov = kernel(X, X)\n",
    "\n",
    "# Draw three samples from the prior\n",
    "samples = np.random.multivariate_normal(mu.ravel(), cov, 3)\n",
    "\n",
    "# Plot GP mean, confidence interval and samples \n",
    "plot_gp(mu, cov, X, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `plot_gp` function is defined [here](gaussian_processes_util.py).\n",
    "\n",
    "### Prediction from noise-free training data\n",
    "\n",
    "To compute the sufficient statistics i.e. mean and covariance of the posterior predictive distribution we implement Equations $(4)$ and $(5)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv\n",
    "\n",
    "def posterior_predictive(X_s, X_train, Y_train, l=1.0, sigma_f=1.0, sigma_y=1e-8):\n",
    "    '''\n",
    "    Computes the suffifient statistics of the GP posterior predictive distribution \n",
    "    from m training data X_train and Y_train and n new inputs X_s.\n",
    "    \n",
    "    Args:\n",
    "        X_s: New input locations (n x d).\n",
    "        X_train: Training locations (m x d).\n",
    "        Y_train: Training targets (m x 1).\n",
    "        l: Kernel length parameter.\n",
    "        sigma_f: Kernel vertical variation parameter.\n",
    "        sigma_y: Noise parameter.\n",
    "    \n",
    "    Returns:\n",
    "        Posterior mean vector (n x d) and covariance matrix (n x n).\n",
    "    '''\n",
    "    K = kernel(X_train, X_train, l, sigma_f) + sigma_y**2 * np.eye(len(X_train))\n",
    "    K_s = kernel(X_train, X_s, l, sigma_f)\n",
    "    K_ss = kernel(X_s, X_s, l, sigma_f) + 1e-8 * np.eye(len(X_s))\n",
    "    K_inv = inv(K)\n",
    "    \n",
    "    # Equation (4)\n",
    "    mu_s = K_s.T.dot(K_inv).dot(Y_train)\n",
    "\n",
    "    # Equation (5)\n",
    "    cov_s = K_ss - K_s.T.dot(K_inv).dot(K_s)\n",
    "    \n",
    "    return mu_s, cov_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and apply them to noise-free training data `X_train` and `Y_train`. The following example draws three samples from the posterior predictive and plots them along with the mean, confidence interval and training data. In a noise-free model, variance at the training points is zero and all random functions drawn from the posterior go through the trainig points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Noise free training data\n",
    "X_train = np.array([-4, -3, -2, -1, 1]).reshape(-1, 1)\n",
    "Y_train = np.sin(X_train)\n",
    "\n",
    "# Compute mean and covariance of the posterior predictive distribution\n",
    "mu_s, cov_s = posterior_predictive(X, X_train, Y_train)\n",
    "\n",
    "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction from noisy training data\n",
    "\n",
    "If some noise is included in the model, training points are only approximated and the variance at the training points is non-zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "noise = 0.4\n",
    "\n",
    "# Noisy training data\n",
    "X_train = np.arange(-3, 4, 1).reshape(-1, 1)\n",
    "Y_train = np.sin(X_train) + noise * np.random.randn(*X_train.shape)\n",
    "\n",
    "# Compute mean and covariance of the posterior predictive distribution\n",
    "mu_s, cov_s = posterior_predictive(X, X_train, Y_train, sigma_y=noise)\n",
    "\n",
    "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of kernel parameters and noise parameter\n",
    "\n",
    "The following example shows the effect of kernel parameters $l$ and $\\sigma_f$ as well as the noise parameter $\\sigma_y$. Higher $l$ values lead to smoother functions and therefore to coarser approximations of the training data. Lower $l$ values make functions more wiggly with wide confidence intervals between training data points. $\\sigma_f$ controls the vertical variation of functions drawn from the GP. This can be seen by the wide confidence intervals outside the training data region in the right figure of the second row. $\\sigma_y$ represents the amount of noise in the training data. Higher $\\sigma_y$ values make more coarse approximations which avoids overfitting to noisy data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "params = [\n",
    "    (0.3, 1.0, 0.2),\n",
    "    (3.0, 1.0, 0.2),\n",
    "    (1.0, 0.3, 0.2),\n",
    "    (1.0, 3.0, 0.2),\n",
    "    (1.0, 1.0, 0.05),\n",
    "    (1.0, 1.0, 1.5),\n",
    "]\n",
    "\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "for i, (l, sigma_f, sigma_y) in enumerate(params):\n",
    "    mu_s, cov_s = posterior_predictive(X, X_train, Y_train, l=l, \n",
    "                                       sigma_f=sigma_f, \n",
    "                                       sigma_y=sigma_y)\n",
    "    plt.subplot(3, 2, i + 1)\n",
    "    plt.subplots_adjust(top=2)\n",
    "    plt.title(f'l = {l}, sigma_f = {sigma_f}, sigma_y = {sigma_y}')\n",
    "    plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal values for these parameters can be estimated by maximizing the log marginal likelihood which is given by<sup>[1][3]</sup>\n",
    "\n",
    "$$\n",
    "\\log p(\\mathbf{y} \\lvert \\mathbf{X}) = \n",
    "\\log \\mathcal{N}(\\mathbf{y} \\lvert \\boldsymbol{0},\\mathbf{K}_y) =\n",
    "-\\frac{1}{2} \\mathbf{y}^T \\mathbf{K}_y^{-1} \\mathbf{y} \n",
    "-\\frac{1}{2} \\log \\begin{vmatrix}\\mathbf{K}_y\\end{vmatrix} \n",
    "-\\frac{N}{2} \\log(2\\pi) \\tag{7}\n",
    "$$\n",
    "\n",
    "In the following we will minimize the negative log marginal likelihood w.r.t. parameters $l$ and $\\sigma_f$, $\\sigma_y$ is set to the known noise level of the data. If the noise level is unknown, $\\sigma_y$ can be estimated as well along with the other parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.linalg import cholesky, det, lstsq\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def nll_fn(X_train, Y_train, noise, naive=True):\n",
    "    '''\n",
    "    Returns a function that computes the negative log marginal\n",
    "    likelihood for training data X_train and Y_train and given \n",
    "    noise level.\n",
    "    \n",
    "    Args:\n",
    "        X_train: training locations (m x d).\n",
    "        Y_train: training targets (m x 1).\n",
    "        noise: known noise level of Y_train.\n",
    "        naive: if True use a naive implementation of Eq. (7), if \n",
    "               False use a numerically more stable implementation. \n",
    "        \n",
    "    Returns:\n",
    "        Minimization objective.\n",
    "    '''\n",
    "    def nll_naive(theta):\n",
    "        # Naive implementation of Eq. (7). Works well for the examples \n",
    "        # in this article but is numerically less stable compared to \n",
    "        # the implementation in nll_stable below.\n",
    "        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \\\n",
    "            noise**2 * np.eye(len(X_train))\n",
    "        return 0.5 * np.log(det(K)) + \\\n",
    "               0.5 * Y_train.T.dot(inv(K).dot(Y_train)) + \\\n",
    "               0.5 * len(X_train) * np.log(2*np.pi)\n",
    "\n",
    "    def nll_stable(theta):\n",
    "        # Numerically more stable implementation of Eq. (7) as described\n",
    "        # in http://www.gaussianprocess.org/gpml/chapters/RW2.pdf, Section\n",
    "        # 2.2, Algorithm 2.1.\n",
    "        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \\\n",
    "            noise**2 * np.eye(len(X_train))\n",
    "        L = cholesky(K)\n",
    "        return np.sum(np.log(np.diagonal(L))) + \\\n",
    "               0.5 * Y_train.T.dot(lstsq(L.T, lstsq(L, Y_train)[0])[0]) + \\\n",
    "               0.5 * len(X_train) * np.log(2*np.pi)\n",
    "    \n",
    "    if naive:\n",
    "        return nll_naive\n",
    "    else:\n",
    "        return nll_stable\n",
    "\n",
    "# Minimize the negative log-likelihood w.r.t. parameters l and sigma_f.\n",
    "# We should actually run the minimization several times with different\n",
    "# initializations to avoid local minima but this is skipped here for\n",
    "# simplicity.\n",
    "res = minimize(nll_fn(X_train, Y_train, noise), [1, 1], \n",
    "               bounds=((1e-5, None), (1e-5, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "# Store the optimization results in global variables so that we can\n",
    "# compare it later with the results from other implementations.\n",
    "l_opt, sigma_f_opt = res.x\n",
    "l_opt, sigma_f_opt\n",
    "\n",
    "# Compute the prosterior predictive statistics with optimized kernel parameters and plot the results\n",
    "mu_s, cov_s = posterior_predictive(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With optimized kernel parameters, training data are reasonably covered by the 95% confidence interval and the mean of the posterior predictive is a good approximation.\n",
    "\n",
    "### Higher dimensions\n",
    "\n",
    "The above implementation can also be used for higher input data dimensions. Here, a GP is used to fit noisy samples from a sine wave originating at $\\boldsymbol{0}$ and expanding in the x-y plane. The following plots show the noisy samples and the posterior predictive mean before and after kernel parameter optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from gaussian_processes_util import plot_gp_2D\n",
    "\n",
    "noise_2D = 0.1\n",
    "\n",
    "rx, ry = np.arange(-5, 5, 0.3), np.arange(-5, 5, 0.3)\n",
    "gx, gy = np.meshgrid(rx, rx)\n",
    "\n",
    "X_2D = np.c_[gx.ravel(), gy.ravel()]\n",
    "\n",
    "X_2D_train = np.random.uniform(-4, 4, (100, 2))\n",
    "Y_2D_train = np.sin(0.5 * np.linalg.norm(X_2D_train, axis=1)) + \\\n",
    "             noise_2D * np.random.randn(len(X_2D_train))\n",
    "\n",
    "plt.figure(figsize=(14,7))\n",
    "\n",
    "mu_s, _ = posterior_predictive(X_2D, X_2D_train, Y_2D_train, sigma_y=noise_2D)\n",
    "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train, \n",
    "           f'Before parameter optimization: l={1.00} sigma_f={1.00}', 1)\n",
    "\n",
    "res = minimize(nll_fn(X_2D_train, Y_2D_train, noise_2D), [1, 1], \n",
    "               bounds=((1e-5, None), (1e-5, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "mu_s, _ = posterior_predictive(X_2D, X_2D_train, Y_2D_train, *res.x, sigma_y=noise_2D)\n",
    "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train,\n",
    "           f'After parameter optimization: l={res.x[0]:.2f} sigma_f={res.x[1]:.2f}', 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the true sine wave is approximated much better after parameter optimization.\n",
    "\n",
    "## Libraries that implement GPs\n",
    "\n",
    "This section shows two examples of libraries that provide implementations of GPs. I'll provide only a minimal setup here, just enough for reproducing the above results. For further details please consult the documentation of these libraries.\n",
    "\n",
    "### Scikit-learn\n",
    "\n",
    "Scikit-learn provides a `GaussianProcessRegressor` for implementing [GP regression models](http://scikit-learn.org/stable/modules/gaussian_process.html#gaussian-process-regression-gpr). It can be configured with [pre-defined kernels and user-defined kernels](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels). Kernels can also be composed. The squared exponential kernel is the `RBF` kernel in scikit-learn. The `RBF` kernel only has a `length_scale` parameter which corresponds to the $l$ parameter above. To have a $\\sigma_f$ parameter as well, we have to compose the `RBF` kernel with a `ConstantKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "from sklearn.gaussian_process.kernels import ConstantKernel, RBF\n",
    "\n",
    "rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)\n",
    "gpr = GaussianProcessRegressor(kernel=rbf, alpha=noise**2)\n",
    "\n",
    "# Reuse training data from previous 1D example\n",
    "gpr.fit(X_train, Y_train)\n",
    "\n",
    "# Compute posterior predictive mean and covariance\n",
    "mu_s, cov_s = gpr.predict(X, return_cov=True)\n",
    "\n",
    "# Obtain optimized kernel parameters\n",
    "l = gpr.kernel_.k2.get_params()['length_scale']\n",
    "sigma_f = np.sqrt(gpr.kernel_.k1.get_params()['constant_value'])\n",
    "\n",
    "# Compare with previous results\n",
    "assert(np.isclose(l_opt, l))\n",
    "assert(np.isclose(sigma_f_opt, sigma_f))\n",
    "\n",
    "# Plot the results\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GPy\n",
    "\n",
    "[GPy](http://sheffieldml.github.io/GPy/) is a Gaussian processes framework from the Sheffield machine learning group. It provides a `GPRegression` class for implementing GP regression models. By default, `GPRegression` also estimates the noise parameter $\\sigma_y$ from data, so we have to `fix()` this parameter to be able to reproduce the above results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 8.119286233766962<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 2<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>              value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right> 0.6078930786683978</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right> 0.9242513823591277</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>0.16000000000000003</td><td class=tg-center> +ve fixed </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7f1d5c416f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import GPy\n",
    "\n",
    "rbf = GPy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0)\n",
    "gpr = GPy.models.GPRegression(X_train, Y_train, rbf)\n",
    "\n",
    "# Fix the noise variance to known value \n",
    "gpr.Gaussian_noise.variance = noise**2\n",
    "gpr.Gaussian_noise.variance.fix()\n",
    "\n",
    "# Run optimization\n",
    "gpr.optimize();\n",
    "\n",
    "# Display optimized parameter values\n",
    "display(gpr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /home/martin/miniconda3/envs/ml/lib/python3.6/site-packages/matplotlib/figure.py:2369: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Obtain optimized kernel parameters\n",
    "l = gpr.rbf.lengthscale.values[0]\n",
    "sigma_f = np.sqrt(gpr.rbf.variance.values[0])\n",
    "\n",
    "# Compare with previous results\n",
    "assert(np.isclose(l_opt, l))\n",
    "assert(np.isclose(sigma_f_opt, sigma_f))\n",
    "\n",
    "# Plot the results with the built-in plot function\n",
    "gpr.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thanks for reading up to here :-) In another article, I'll show how Gaussian processes can be used for black-box optimization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "\\[1\\] Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapters 4, 14 and 15.  \n",
    "\\[2\\] Christopher M. Bishop. [Pattern Recognition and Machine Learning](http://www.springer.com/de/book/9780387310732), Chapter 6.  \n",
    "\\[3\\] Carl Edward Rasmussen and Christopher K. I. Williams. [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/).  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
